Today, in the case of motor vehicles, especially in regard to commercial vehicles, more and more cameras are being installed for the purpose of monitoring the area surrounding the vehicle. Panoramic cameras of types to serve such a purpose are rigidly affixed to a vehicle so that the camera has to encompass a wide area of sight or a wide-angled field of view. For this purpose cameras with comparatively inexpensive wide-angle objective lens systems are customarily installed.
These wide-angle objective lenses encompass a very wide field angle of 100° or more. However, this large field angle, i.e., this extensive extent of view, must be bought at the price of considerable distortion and reduced brightness in the outer edges of the displayed image. “Distortion” or “image distortion,” means that straight lines in the edge areas of the object show themselves as curved in the produced image. It is important to distinguish a barrel-shaped distortion and a cushion-shaped distortion. Wide-angle lens systems usually show a barrel-shaped distortion, i.e., expressed as positive figure. FIG. 3 illustrates examples of positive and negative image distortions. Image distortion is expressed as {(y′−y)/y′}, where y′ represents the height of the image without distortion and y designates the height of the image with aberration. As a general rule, only the radial distortion, i.e., the change in lengths along radial distances, are considered. In the present application %-values for distortion designate this radial image distortion.
Where objective lenses are involved, and especially wide-angle objective lenses, a multiplicity of errors or aberrations in the produced images occur, which are known as the “Seven Seidel Aberrations” referring to the Seidel Error Theory. These seven Seidel Aberrations can be combined into three groups:
I) focus aberrations
a) Spherical aberration, (differences in paraxial rays and marginal rays),
b) coma, (light patching, with stringed tails),
c) astigmatism, (formation of focal lines at points),
II) positional aberrations
d) field curvature, (result of curved surface of image receiver),
e) distortion, (convex or concave forms of outlines or barrel-shaped or cushion shaped outlines),
III) color aberration
f) longitudinal color aberration, and
g) transverse color aberration.
Each lens of an objective lens system possesses various properties such as the kind of glass, curvature expressed by the radii of the two lens surfaces) and the thickness of the lens. The arrangement of a plurality of lenses in an objective system becomes characterized by the separation distance of one lens from another, the position of an iris, and the back focus, i.e., the distance of the last lens surface to the plane of the recorded image. These characteristics become known as parameters or degrees of freedom. Theoretically, each of these degrees of freedom can be put to use to correct image aberrations. Contrary thereto, each degree of freedom takes part in all image aberrations. By customary use of optics software the proportionate image aberration for each single lens surface can be calculated.
In the following the work method of an optics designer will be explained by the aid of a pertinent example. This example is very important because it presents the concept of how an optics-designer proceeds, and it shows how decisive the creativity of the optics designer still is. It is possible to correct the seven aberrations with a minimum of eight independent system parameters. Focal length is also such a parameter. A triplet, i.e., a three-lens objective, could, as far as principle is concerned, suffice in this correction. A triplet is normally built-up from two converging outside members, e.g., made of crown glass, and one inner diverging member, e.g., made of flint glass. This assembly provides six radii and two distances between the individual lenses. To start with, the optics designer brings together optical system parameters such as the type of the glass, the thickness of the lenses, the separating distance between the lenses and also the radius of curvature of the glass surfaces. We have six lens surfaces, and it is now possible to determine to what extent each contributes to the overall aberration in the final image. Very simplified, we can determine that in a given case the radius of the second surface of the first lens produces a spherical and chromatic aberration, and the radii of the third lens surfaces produce coma and astigmatism.
The optics designer must now make a decision as to how these aberrations are to be corrected. He may try to change the curvature of the first lens in order to correct for the spherical aberration. However, the curvature of the lens is also decisive for the focal length, and the focal length should not be changed. The change of the curvature may reduce the spherical aberration, but at the same time coma would be increased. The designer can also decide that the correction is to be distributed over a plurality of system parameters in order to ameliorate the erroneous sensitivity. If a specific parameter is very decisive in order to correct for a certain aberration, difficulties arise if the parameter is outside the allowed tolerance or clearance range during the production of the lens system. Or one can also determine that the clearance is too finely specified and cannot be achieved in the production of the lens system.
The optics designer will alter the system parameters up to such a point that the remaining optical aberrations are small enough. In additional steps, he will attempt to correct each image aberration with different degrees of freedom simultaneously. The burden of the correction can then be distributed over the various lens surfaces and the entire system is no longer as critical. Within certain limitations, the optics designer has the possibility of specifying the types of glass and the degrees of curvature, although each chosen combination brings forth another aspect of the total correction. If the triplet has been so configured that it approximates the pre-defined requirements, then the designer can, for example, determine that the astigmatism at the edge of the image has nearly vanished, but appears to play an important role in the inner field of view. At this point, we collide with a new problem. The seven Seidel aberrations, outlined above, are, unfortunately, not the only optical aberrations. One designates the Aberrations of Seidel as “Image aberrations of the Third Order”. Logically, there are more aberrations of a higher order. The most important of these are the aberrations of the fifth and seventh order. These aberration groups are generally only to be encountered when the first group, the “third order” aberrations, is properly corrected.
Theoretically, a very small point existing in the object is mapped into a very small point again. As a matter of practice, this does not occur because of the optical aberrations. A point will not reproduce as a point, but rather as a small disk with a varying distribution of brightness. As soon as these disks under-step a certain diameter, then the image errors become evident. That is a very simplified explanation. In reality, these aberrations are continually in force, but come to attention only if the residual aberrations of the third order are small.
The example given, i.e., the “Triplet Example”, wherein the astigmatism in the field is still visible, shows the effect of these image aberrations of higher orders. One can make use of a defined and entirely controlled residue of the Seidel image aberrations in order to compensate for errors or aberrations of the fifth and seventh order. This is naturally a limited measure and a triplet will have only an acceptable image quality if the field angle and/or the iris opening is small.
It is important to note that a defined optical system, defined by the number and the configuration of the lenses etc., provides for limited correction possibilities. That means, in other words, even with sophisticated optics software and computer power only an experienced optics designer will choose the “correct” starting parameters.
Computers, software and numerical methods are used in order to reduce optical aberrations. This equipment and procedures are be employed in order to optimize an optical system. This huge amount of data may cause its own problems. As a result, the task of the experts or optics designers has not become easier. Rather with the aid of computers an optics designer can consider more parameters and carry out the computations quicker and with greater accuracy.
A certain relationship exists between the number of design parameters of an optical system (lens curvature, lens thickness, distance of separation, refractive index etc.) and the degree of correction of the optical aberrations. With a greater degree of freedom and more design parameters, respectively, the optics designer has correspondingly more possibilities of correcting a system. If an optics designer applies a greater number of optical elements, then a better degree of correction can be attained. This, however, results in a considerable increase in costs, and further, the system may react strongly on the part of manufacturing clearances or increases in weight.
The designer of an optical system must then acquire a very good understanding of the fundamental optical possibilities of a given construction. All constructions or designs require an optimization system or plan in accord with a initial sketch. If the construction is not suitable for a fine compensation of aberrations, then the optics designer will attain only a product of lower quality.
A six-lens objective system has 10 free lens surfaces (radii), six lens thicknesses (one per lens) with four separation-distances between the lenses. Additionally, each kind of glass has its own refractive index and dispersion number to consider. Further, it is necessary to determine the exact position of the iris. With these 36 parameters, i.e., degrees of freedom, the optics designer must correct more than 60 different image aberrations. Each parameter can present something like 10,000 individual values and one must calculate some 6,000 different ray paths for each parameter change.
These 36 degrees of freedom or parameters are also not entirely independent. Some must be combined; others are strongly limited by other parameters. Accordingly, the 36 degrees of freedom are reduced to something like 20, whereby the task becomes even more complex. In view of the given conditions and considerations, it is not surprising that hundreds if not thousands of designs may result, all of which are very close or similar to the desired solution or design. The complete evaluation of a six-lens objective system with the aid of fast computers and software that are able to calculate 10,000 lens surfaces per second takes approximately ten years.
Obviously, such a procedure is not feasible. In order to seek out the best solution to this unending succession of choices, the optics designer must have an inherent recognition of all the effects of the image aberrations on the final image quality of the displayed image. In addition, he must have the capability, to know those factors of image quality that can produce the desired features of the optical system.
In a case of the application of wide angle objective lenses for the panoramic viewing of the immediate environment about a vehicle, there should be, first, the ability to encompass the greatest possible field of view because the cameras are normally affixed rigidly to the vehicle. Second, the image aberrations that will necessarily appear must not deteriorate the recognition of obstacles within the field of view of the wide-angle lens system. Moreover, a wide-angle objective lens system cannot be designed in too complex a manner, since then it would be too expensive for use in a motor vehicle.
Thus it is an object of the present invention to make available an economical, wide-angle objective lens having image aberrations or errors that do not deteriorate the detection of obstructions or obstacles in its field of view. It is a further object of the present invention to provide a camera with such a wide-angle lens system.